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Multiple Access Techniques for
Wireless Communication
FDMA
TDMA
SDMA
PDMA
A Presentation by Schäffner Harald
Introduction
• many users at same time
• share a finite amount of radio spectrum
• high performance
• duplexing generally required
• frequency domain
• time domain
Frequency division duplexing (FDD)
• two bands of frequencies for every user
• forward band
• reverse band
• duplexer needed
• frequency seperation between forward band
and reverse band is constant
frequency seperation
reverse channel forward channel
f
Time division duplexing (TDD)
• uses time for forward and reverse link
• multiple users share a single radio channel
• forward time slot
• reverse time slot
• no duplexer is required
time seperation
t
forward channel
reverse channel
Multiple Access Techniques
• Frequency division multiple access (FDMA)
• Time division multiple access (TDMA)
• Code division multiple access (CDMA)
• Space division multiple access (SDMA)
• grouped as:
• narrowband systems
• wideband systems
Narrowband systems
• large number of narrowband channels
• usually FDD
• Narrowband FDMA
• Narrowband TDMA
• FDMA/FDD
• FDMA/TDD
• TDMA/FDD
• TDMA/TDD
Logical separation FDMA/FDD
f
t
user 1
user n
forward channel
reverse channel
forward channel
reverse channel
...
Logical separation FDMA/TDD
f
t
user 1
user n
forward channel reverse channel
forward channel reverse channel
...
Logical separation TDMA/FDD
f
t
user 1 user n
forward
channel
reverse
channel
forward
channel
reverse
channel
...
Logical separation TDMA/TDD
f
t
user 1 user n
forward
channel
reverse
channel
forward
channel
reverse
channel
...
Wideband systems
• large number of transmitters on one channel
• TDMA techniques
• CDMA techniques
• FDD or TDD multiplexing techniques
• TDMA/FDD
• TDMA/TDD
• CDMA/FDD
• CDMA/TDD
Logical separation CDMA/FDD
code
f
user 1
user n
forward channel reverse channel
forward channel reverse channel
...
Logical separation CDMA/TDD
code
t
user 1
user n
forward channel reverse channel
forward channel reverse channel
...
Multiple Access Techniques in use
Multiple Access
Technique
Advanced Mobile Phone System (AMPS) FDMA/FDD
Global System for Mobile (GSM) TDMA/FDD
US Digital Cellular (USDC) TDMA/FDD
Digital European Cordless Telephone (DECT) FDMA/TDD
US Narrowband Spread Spectrum (IS-95) CDMA/FDD
Cellular System
Frequency division multiple access FDMA
• one phone circuit per channel
• idle time causes wasting of resources
• simultaneously and continuously
transmitting
• usually implemented in narrowband systems
• for example: in AMPS is a FDMA bandwidth
of 30 kHz implemented
FDMA compared to TDMA
• fewer bits for synchronization
• fewer bits for framing
• higher cell site system costs
• higher costs for duplexer used in base
station and subscriber units
• FDMA requires RF filtering to minimize
adjacent channel interference
Nonlinear Effects in FDMA
• many channels - same antenna
• for maximum power efficiency operate near
saturation
• near saturation power amplifiers are
nonlinear
• nonlinearities causes signal spreading
• intermodulation frequencies
Nonlinear Effects in FDMA
• IM are undesired harmonics
• interference with other channels in the
FDMA system
• decreases user C/I - decreases performance
• interference outside the mobile radio band:
adjacent-channel interference
• RF filters needed - higher costs
Number of channels in a FDMA system
• N … number of channels
• Bt … total spectrum allocation
• Bguard … guard band
• Bc … channel bandwidth
N=
Bt - Bguard
Bc
Example: Advanced Mobile Phone System
• AMPS
• FDMA/FDD
• analog cellular system
• 12.5 MHz per simplex band - Bt
• Bguard = 10 kHz ; Bc = 30 kHz
N=
12.5E6 - 2*(10E3)
30E3
= 416 channels
Time Division Multiple Access
• time slots
• one user per slot
• buffer and burst method
• noncontinuous transmission
• digital data
• digital modulation
Slot 1 Slot 2 Slot 3 … Slot N
Repeating Frame Structure
Preamble Information Message Trail Bits
One TDMA Frame
Trail Bits Sync. Bits Information Data Guard Bits
The frame is cyclically repeated over time.
Features of TDMA
• a single carrier frequency for several users
• transmission in bursts
• low battery consumption
• handoff process much simpler
• FDD : switch instead of duplexer
• very high transmission rate
• high synchronization overhead
• guard slots necessary
Number of channels in a TDMA system
• N … number of channels
• m … number of TDMA users per radio channel
• Btot … total spectrum allocation
• Bguard … Guard Band
• Bc … channel bandwidth
N=
m*(Btot - 2*Bguard)
Bc
Example: Global System for Mobile (GSM)
• TDMA/FDD
• forward link at Btot = 25 MHz
• radio channels of Bc = 200 kHz
• if m = 8 speech channels supported, and
• if no guard band is assumed :
N= 8*25E6
200E3
= 1000 simultaneous users
Efficiency of TDMA
• percentage of transmitted data that contain
information
• frame efficiency f
• usually end user efficiency < f ,
• because of source and channel coding
• How get f ?
Slot 1 Slot 2 Slot 3 … Slot N
Repeating Frame Structure
Preamble Information Message Trail Bits
One TDMA Frame
Trail Bits Sync. Bits Information Data Guard Bits
The frame is cyclically repeated over time.
Efficiency of TDMA
• bOH … number of overhead bits
• Nr … number of reference bursts per frame
• br … reference bits per reference burst
• Nt … number of traffic bursts per frame
• bp … overhead bits per preamble in each slot
• bg … equivalent bits in each guard time
intervall
bOH = Nr*br + Nt*bp + Nt*bg + Nr*bg
Efficiency of TDMA
bT = Tf * R
• bT … total number of bits per frame
• Tf … frame duration
• R … channel bit rate
Efficiency of TDMA
• f … frame efficiency
• bOH … number of overhead bits per frame
• bT … total number of bits per frame
f = (1-bOH/bT)*100%
Space Division Multiple Access
• Controls radiated energy for each user in space
• using spot beam antennas
• base station tracks user when moving
• cover areas with same frequency:
• TDMA or CDMA systems
• cover areas with same frequency:
• FDMA systems
Space Division Multiple Access
• primitive applications are
“Sectorized antennas”
• in future adaptive
antennas simultaneously
steer energy in the
direction of many users at
once
Reverse link problems
• general problem
• different propagation path from user to base
• dynamic control of transmitting power from
each user to the base station required
• limits by battery consumption of subscriber
units
• possible solution is a filter for each user
Solution by SDMA systems
• adaptive antennas promise to mitigate
reverse link problems
• limiting case of infinitesimal beamwidth
• limiting case of infinitely fast track ability
• thereby unique channel that is free from
interference
• all user communicate at same time using the
same channel
Disadvantage of SDMA
• perfect adaptive antenna system:
infinitely large antenna needed
• compromise needed
SDMA and PDMA in satellites
• INTELSAT IVA
• SDMA dual-beam
receive antenna
• simultaneously access
from two different
regions of the earth
SDMA and PDMA in satellites
• COMSTAR 1
• PDMA
• separate antennas
• simultaneously
access from same
region
SDMA and PDMA in satellites
• INTELSAT V
• PDMA and SDMA
• two hemispheric
coverages by SDMA
• two smaller beam
zones by PDMA
• orthogonal polarization
Capacity of Cellular Systems
• channel capacity: maximum number of users
in a fixed frequency band
• radio capacity : value for spectrum efficiency
• reverse channel interference
• forward channel interference
• How determine the radio capacity?
Co-Channel Reuse Ratio Q
• Q … co-channel reuse ratio
• D … distance between two co-channel cells
• R … cell radius
Q=D/R
Forward channel interference
• cluster size of 4
• D0 … distance
serving station
to user
• DK … distance
co-channel base
station to user
Carrier-to-interference ratio C/I
• M closest co-channels cells cause first order
interference
C
=
I
D0
-n0
M
k=1
DK
-nk
• n0 … path loss exponent in the desired cell
• nk … path loss exponent to the interfering
base station
Carrier-to-interference ratio C/I
• Assumption:
• just the 6 closest stations interfere
• all these stations have the same distance D
• all have similar path loss exponents to n0
C
I
=
D0
-n
6*D
-n
Worst Case Performance
• maximum interference at D0 = R
• (C/I)min for acceptable signal quality
• following equation must hold:
1/6 * (R/D) (C/I)min
=
>
-n
Co-Channel reuse ratio Q
• D … distance of the 6 closest interfering
base stations
• R … cell radius
• (C/I)min … minimum carrier-to-interference
ratio
• n … path loss exponent
Q = D/R = (6*(C/I)min)
1/n
Radio Capacity m
• Bt … total allocated spectrum for the system
• Bc … channel bandwidth
• N … number of cells in a complete frequency
reuse cluster
m =
Bt
Bc * N
radio channels/cell
Radio Capacity m
• N is related to the co-channel factor Q by:
Q = (3*N)
1/2
m=
Bt
Bc * (Q²/3)
=
Bt
Bc *
6 C
I
3n/2
( *( )min
)
2/n
Radio Capacity m for n = 4
• m … number of radio channels per cell
• (C/I)min lower in digital systems compared to
analog systems
• lower (C/I)min imply more capacity
• exact values in real world conditions measured
m =
Bt
Bc * 2/3 * (C/I)min
Compare different Systems
• each digital wireless standard has different
(C/I)min
• to compare them an equivalent (C/I) needed
• keep total spectrum allocation Bt and
number of rario channels per cell m
constant to get (C/I)eq :
Compare different Systems
• Bc … bandwidth of a particular system
• (C/I)min … tolerable value for the same system
• Bc’ … channel bandwidth for a different
system
• (C/I)eq … minimum C/I value for the different
system
C
I
= C
I
Bc
Bc’
( ) ( )
min
)²
eq * (
C/I in digital cellular systems
• Rb … channel bit rate
• Eb … energy per bit
• Rc … rate of the channel code
• Ec … energy per code symbol
C Eb*Rb Ec*Rc
I I I
= =
C/I in digital cellular systems
• combine last two equations:
(C/I) (Ec*Rc)/I Bc’
(C/I)eq (Ec’*Rc’)/I’ Bc
= = ( )²
• The sign ‘ marks compared system
parameters
C/I in digital cellular systems
• Relationship between Rc and Bc is always
linear (Rc/Rc’ = Bc/Bc’ )
• assume that level I is the same for two
different systems ( I’ = I ) :
Ec Bc’
Ec‘ Bc
= ( )³
Compare C/I between FDMA and TDMA
• Assume that multichannel FDMA system
occupies same spectrum as a TDMA system
• FDMA : C = Eb * Rb ; I = I0 * Bc
• TDMA : C’ = Eb * Rb’ ; I’ = I0 * Bc’
• Eb … Energy per bit
• I0 … interference power per Hertz
• Rb … channel bit rate
• Bc … channel bandwidth
Example
• A FDMA system has 3 channels , each with
a bandwidth of 10kHz and a transmission
rate of 10 kbps.
• A TDMA system has 3 time slots, a channel
bandwidth of 30kHz and a transmission rate
of 30 kbps.
• What’s the received carrier-to-interference
ratio for a user ?
Example
• In TDMA system C’/I’ be measured in
333.3 ms per second - one time slot
C’ = Eb*Rb’ = 1/3*(Eb*10E4 bits) = 3*Rb*Eb=3*C
I’ = I0*Bc’ = I0*30kHz = 3*I
• In this example FDMA and TDMA have the
same radio capacity (C/I leads to m)
Example
• Peak power of TDMA is 10logk higher then
in FDMA ( k … time slots)
• in practice TDMA have a 3-6 times better
capacity
Capacity of SDMA systems
• one beam each user
• base station tracks each user as it moves
• adaptive antennas most powerful form
• beam pattern G() has maximum gain in
the direction of desired user
• beam is formed by N-element adaptive
array antenna
Capacity of SDMA systems
• G() steered in the horizontal  -plane
through 360°
• G() has no variation in the elevation plane
to account which are near to and far from the
base station
• following picture shows a 60 degree
beamwidth with a 6 dB sideslope level
Capacity of SDMA systems
Capacity of SDMA systems
• reverse link received signal power, from
desired mobiles, is Pr;0
• interfering users i = 1,…,k-1 have received
power Pr;I
• average total interference power I seen by a
single desired user:
Capacity of SDMA
• i … direction of the i-th user in the
horizontal plane
• E … expectation operator
I = E {  G(i) Pr;I}
K-1
i=1
Capacity of SDMA systems
• in case of perfect power control (received
power from each user is the same) :
Pr;I = Pc
• Average interference power seen by user 0:
I = Pc E {  G(i) }
K-1
i=1
Capacity of SDMA systems
• users independently and identically
distributed throughout the cell:
I = Pc *(k -1) * 1/D
• D … directivity of the antenna - given by
max(G())
• D typ. 3dB …10dB
Pb = Q ( )
Capacity of SDMA systems
• Average bit error rate Pb for user 0:
3 D N
K-1
• D … directivity of the antenna
• Q(x) … standard Q-function
• N … spreading factor
• K … number of users in a cell
Capacity of SDMA systems

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schaeffner.ppt

  • 1. Multiple Access Techniques for Wireless Communication FDMA TDMA SDMA PDMA A Presentation by Schäffner Harald
  • 2. Introduction • many users at same time • share a finite amount of radio spectrum • high performance • duplexing generally required • frequency domain • time domain
  • 3. Frequency division duplexing (FDD) • two bands of frequencies for every user • forward band • reverse band • duplexer needed • frequency seperation between forward band and reverse band is constant frequency seperation reverse channel forward channel f
  • 4. Time division duplexing (TDD) • uses time for forward and reverse link • multiple users share a single radio channel • forward time slot • reverse time slot • no duplexer is required time seperation t forward channel reverse channel
  • 5. Multiple Access Techniques • Frequency division multiple access (FDMA) • Time division multiple access (TDMA) • Code division multiple access (CDMA) • Space division multiple access (SDMA) • grouped as: • narrowband systems • wideband systems
  • 6. Narrowband systems • large number of narrowband channels • usually FDD • Narrowband FDMA • Narrowband TDMA • FDMA/FDD • FDMA/TDD • TDMA/FDD • TDMA/TDD
  • 7. Logical separation FDMA/FDD f t user 1 user n forward channel reverse channel forward channel reverse channel ...
  • 8. Logical separation FDMA/TDD f t user 1 user n forward channel reverse channel forward channel reverse channel ...
  • 9. Logical separation TDMA/FDD f t user 1 user n forward channel reverse channel forward channel reverse channel ...
  • 10. Logical separation TDMA/TDD f t user 1 user n forward channel reverse channel forward channel reverse channel ...
  • 11. Wideband systems • large number of transmitters on one channel • TDMA techniques • CDMA techniques • FDD or TDD multiplexing techniques • TDMA/FDD • TDMA/TDD • CDMA/FDD • CDMA/TDD
  • 12. Logical separation CDMA/FDD code f user 1 user n forward channel reverse channel forward channel reverse channel ...
  • 13. Logical separation CDMA/TDD code t user 1 user n forward channel reverse channel forward channel reverse channel ...
  • 14. Multiple Access Techniques in use Multiple Access Technique Advanced Mobile Phone System (AMPS) FDMA/FDD Global System for Mobile (GSM) TDMA/FDD US Digital Cellular (USDC) TDMA/FDD Digital European Cordless Telephone (DECT) FDMA/TDD US Narrowband Spread Spectrum (IS-95) CDMA/FDD Cellular System
  • 15. Frequency division multiple access FDMA • one phone circuit per channel • idle time causes wasting of resources • simultaneously and continuously transmitting • usually implemented in narrowband systems • for example: in AMPS is a FDMA bandwidth of 30 kHz implemented
  • 16. FDMA compared to TDMA • fewer bits for synchronization • fewer bits for framing • higher cell site system costs • higher costs for duplexer used in base station and subscriber units • FDMA requires RF filtering to minimize adjacent channel interference
  • 17. Nonlinear Effects in FDMA • many channels - same antenna • for maximum power efficiency operate near saturation • near saturation power amplifiers are nonlinear • nonlinearities causes signal spreading • intermodulation frequencies
  • 18. Nonlinear Effects in FDMA • IM are undesired harmonics • interference with other channels in the FDMA system • decreases user C/I - decreases performance • interference outside the mobile radio band: adjacent-channel interference • RF filters needed - higher costs
  • 19. Number of channels in a FDMA system • N … number of channels • Bt … total spectrum allocation • Bguard … guard band • Bc … channel bandwidth N= Bt - Bguard Bc
  • 20. Example: Advanced Mobile Phone System • AMPS • FDMA/FDD • analog cellular system • 12.5 MHz per simplex band - Bt • Bguard = 10 kHz ; Bc = 30 kHz N= 12.5E6 - 2*(10E3) 30E3 = 416 channels
  • 21. Time Division Multiple Access • time slots • one user per slot • buffer and burst method • noncontinuous transmission • digital data • digital modulation
  • 22. Slot 1 Slot 2 Slot 3 … Slot N Repeating Frame Structure Preamble Information Message Trail Bits One TDMA Frame Trail Bits Sync. Bits Information Data Guard Bits The frame is cyclically repeated over time.
  • 23. Features of TDMA • a single carrier frequency for several users • transmission in bursts • low battery consumption • handoff process much simpler • FDD : switch instead of duplexer • very high transmission rate • high synchronization overhead • guard slots necessary
  • 24. Number of channels in a TDMA system • N … number of channels • m … number of TDMA users per radio channel • Btot … total spectrum allocation • Bguard … Guard Band • Bc … channel bandwidth N= m*(Btot - 2*Bguard) Bc
  • 25. Example: Global System for Mobile (GSM) • TDMA/FDD • forward link at Btot = 25 MHz • radio channels of Bc = 200 kHz • if m = 8 speech channels supported, and • if no guard band is assumed : N= 8*25E6 200E3 = 1000 simultaneous users
  • 26. Efficiency of TDMA • percentage of transmitted data that contain information • frame efficiency f • usually end user efficiency < f , • because of source and channel coding • How get f ?
  • 27. Slot 1 Slot 2 Slot 3 … Slot N Repeating Frame Structure Preamble Information Message Trail Bits One TDMA Frame Trail Bits Sync. Bits Information Data Guard Bits The frame is cyclically repeated over time.
  • 28. Efficiency of TDMA • bOH … number of overhead bits • Nr … number of reference bursts per frame • br … reference bits per reference burst • Nt … number of traffic bursts per frame • bp … overhead bits per preamble in each slot • bg … equivalent bits in each guard time intervall bOH = Nr*br + Nt*bp + Nt*bg + Nr*bg
  • 29. Efficiency of TDMA bT = Tf * R • bT … total number of bits per frame • Tf … frame duration • R … channel bit rate
  • 30. Efficiency of TDMA • f … frame efficiency • bOH … number of overhead bits per frame • bT … total number of bits per frame f = (1-bOH/bT)*100%
  • 31. Space Division Multiple Access • Controls radiated energy for each user in space • using spot beam antennas • base station tracks user when moving • cover areas with same frequency: • TDMA or CDMA systems • cover areas with same frequency: • FDMA systems
  • 32. Space Division Multiple Access • primitive applications are “Sectorized antennas” • in future adaptive antennas simultaneously steer energy in the direction of many users at once
  • 33. Reverse link problems • general problem • different propagation path from user to base • dynamic control of transmitting power from each user to the base station required • limits by battery consumption of subscriber units • possible solution is a filter for each user
  • 34. Solution by SDMA systems • adaptive antennas promise to mitigate reverse link problems • limiting case of infinitesimal beamwidth • limiting case of infinitely fast track ability • thereby unique channel that is free from interference • all user communicate at same time using the same channel
  • 35. Disadvantage of SDMA • perfect adaptive antenna system: infinitely large antenna needed • compromise needed
  • 36. SDMA and PDMA in satellites • INTELSAT IVA • SDMA dual-beam receive antenna • simultaneously access from two different regions of the earth
  • 37. SDMA and PDMA in satellites • COMSTAR 1 • PDMA • separate antennas • simultaneously access from same region
  • 38. SDMA and PDMA in satellites • INTELSAT V • PDMA and SDMA • two hemispheric coverages by SDMA • two smaller beam zones by PDMA • orthogonal polarization
  • 39. Capacity of Cellular Systems • channel capacity: maximum number of users in a fixed frequency band • radio capacity : value for spectrum efficiency • reverse channel interference • forward channel interference • How determine the radio capacity?
  • 40. Co-Channel Reuse Ratio Q • Q … co-channel reuse ratio • D … distance between two co-channel cells • R … cell radius Q=D/R
  • 41. Forward channel interference • cluster size of 4 • D0 … distance serving station to user • DK … distance co-channel base station to user
  • 42. Carrier-to-interference ratio C/I • M closest co-channels cells cause first order interference C = I D0 -n0 M k=1 DK -nk • n0 … path loss exponent in the desired cell • nk … path loss exponent to the interfering base station
  • 43. Carrier-to-interference ratio C/I • Assumption: • just the 6 closest stations interfere • all these stations have the same distance D • all have similar path loss exponents to n0 C I = D0 -n 6*D -n
  • 44. Worst Case Performance • maximum interference at D0 = R • (C/I)min for acceptable signal quality • following equation must hold: 1/6 * (R/D) (C/I)min = > -n
  • 45. Co-Channel reuse ratio Q • D … distance of the 6 closest interfering base stations • R … cell radius • (C/I)min … minimum carrier-to-interference ratio • n … path loss exponent Q = D/R = (6*(C/I)min) 1/n
  • 46. Radio Capacity m • Bt … total allocated spectrum for the system • Bc … channel bandwidth • N … number of cells in a complete frequency reuse cluster m = Bt Bc * N radio channels/cell
  • 47. Radio Capacity m • N is related to the co-channel factor Q by: Q = (3*N) 1/2 m= Bt Bc * (Q²/3) = Bt Bc * 6 C I 3n/2 ( *( )min ) 2/n
  • 48. Radio Capacity m for n = 4 • m … number of radio channels per cell • (C/I)min lower in digital systems compared to analog systems • lower (C/I)min imply more capacity • exact values in real world conditions measured m = Bt Bc * 2/3 * (C/I)min
  • 49. Compare different Systems • each digital wireless standard has different (C/I)min • to compare them an equivalent (C/I) needed • keep total spectrum allocation Bt and number of rario channels per cell m constant to get (C/I)eq :
  • 50. Compare different Systems • Bc … bandwidth of a particular system • (C/I)min … tolerable value for the same system • Bc’ … channel bandwidth for a different system • (C/I)eq … minimum C/I value for the different system C I = C I Bc Bc’ ( ) ( ) min )² eq * (
  • 51. C/I in digital cellular systems • Rb … channel bit rate • Eb … energy per bit • Rc … rate of the channel code • Ec … energy per code symbol C Eb*Rb Ec*Rc I I I = =
  • 52. C/I in digital cellular systems • combine last two equations: (C/I) (Ec*Rc)/I Bc’ (C/I)eq (Ec’*Rc’)/I’ Bc = = ( )² • The sign ‘ marks compared system parameters
  • 53. C/I in digital cellular systems • Relationship between Rc and Bc is always linear (Rc/Rc’ = Bc/Bc’ ) • assume that level I is the same for two different systems ( I’ = I ) : Ec Bc’ Ec‘ Bc = ( )³
  • 54. Compare C/I between FDMA and TDMA • Assume that multichannel FDMA system occupies same spectrum as a TDMA system • FDMA : C = Eb * Rb ; I = I0 * Bc • TDMA : C’ = Eb * Rb’ ; I’ = I0 * Bc’ • Eb … Energy per bit • I0 … interference power per Hertz • Rb … channel bit rate • Bc … channel bandwidth
  • 55. Example • A FDMA system has 3 channels , each with a bandwidth of 10kHz and a transmission rate of 10 kbps. • A TDMA system has 3 time slots, a channel bandwidth of 30kHz and a transmission rate of 30 kbps. • What’s the received carrier-to-interference ratio for a user ?
  • 56. Example • In TDMA system C’/I’ be measured in 333.3 ms per second - one time slot C’ = Eb*Rb’ = 1/3*(Eb*10E4 bits) = 3*Rb*Eb=3*C I’ = I0*Bc’ = I0*30kHz = 3*I • In this example FDMA and TDMA have the same radio capacity (C/I leads to m)
  • 57. Example • Peak power of TDMA is 10logk higher then in FDMA ( k … time slots) • in practice TDMA have a 3-6 times better capacity
  • 58. Capacity of SDMA systems • one beam each user • base station tracks each user as it moves • adaptive antennas most powerful form • beam pattern G() has maximum gain in the direction of desired user • beam is formed by N-element adaptive array antenna
  • 59. Capacity of SDMA systems • G() steered in the horizontal  -plane through 360° • G() has no variation in the elevation plane to account which are near to and far from the base station • following picture shows a 60 degree beamwidth with a 6 dB sideslope level
  • 60. Capacity of SDMA systems
  • 61. Capacity of SDMA systems • reverse link received signal power, from desired mobiles, is Pr;0 • interfering users i = 1,…,k-1 have received power Pr;I • average total interference power I seen by a single desired user:
  • 62. Capacity of SDMA • i … direction of the i-th user in the horizontal plane • E … expectation operator I = E {  G(i) Pr;I} K-1 i=1
  • 63. Capacity of SDMA systems • in case of perfect power control (received power from each user is the same) : Pr;I = Pc • Average interference power seen by user 0: I = Pc E {  G(i) } K-1 i=1
  • 64. Capacity of SDMA systems • users independently and identically distributed throughout the cell: I = Pc *(k -1) * 1/D • D … directivity of the antenna - given by max(G()) • D typ. 3dB …10dB
  • 65. Pb = Q ( ) Capacity of SDMA systems • Average bit error rate Pb for user 0: 3 D N K-1 • D … directivity of the antenna • Q(x) … standard Q-function • N … spreading factor • K … number of users in a cell
  • 66. Capacity of SDMA systems